I see absolutely no reason to think that this is true. As you said, you can't prove the negative, whether or not the Sox would have drawn any better at the gate if they were in Addison (everything else being equal). Sure, your sister in Arlington Heights might have an easier time getting to games. But, lots of those families originally from the south side moved to southern suburbs. It wouldn't be any easier to get to Addison from Oak Lawn than it is to get to Bridgeport from Oak Lawn.

Those demographic studies would have been done in 1986. The city has changed drastically since then, with lots of gentrification and people (read: money) moving back to the city. As the economic and housing crisis has, arguably, hurt suburbia and exurbia moreso than the city itself, I suspect that a suburban ballpark would also be worse off in these last few years than an urban park. Those demographic shifts from city to suburbia/exurbia in the last few decades are not unique to the Chicagoland area. Despite that, there has been a movement in new ballpark construction from suburb to city, not the other way around. I think there is a good reason behind that.

Neither of us can prove our points but the fact remains the Sox for a big market team have drawn I would say at best mediocre in the new park. First place most of last year and 24th in MLB attendance. That's pathetic.
As far as the other cities none of them have to contend with the darlings from the Northside. I may be wrong but there aren't any teams that are located in the suburbs except for LAA and Texas and no other ones moved out of the city except them, the Rangers from the start were in Arlington. Marlins come close but they would have been better off building next door to Dolphin Stadium.